Those feelings go both ways, which is why the LEOs need to coordinate with civilians, and make sure it is very clear that they are LEOs when they approach civilians - particularly if they too are holding weapons instead of just having a holstered side arm.
Brash statements from either side aren't smart. What is needed is cooperation, coordination, and very clear identification of LEOs.
I see no reason for private citizens like myself to be making armed patrols of public property. I run, ride horses & hike on public land. If I see some guys with rifles who are not acting like hunters, my first thought would be “Drug dealers”. And if I have a gun with me, my instinct would be to use my gun to cover my retreat.
I also go out shooting in the desert. I’ve met armed guys planning to use the same general area for target practice. Again, the context - in daytime, in an area suitable for target shooting - makes a difference.